Properties

Label 143.2.h.b.92.1
Level $143$
Weight $2$
Character 143.92
Analytic conductor $1.142$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [143,2,Mod(14,143)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(143, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([8, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("143.14");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 143 = 11 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 143.h (of order \(5\), degree \(4\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(1.14186074890\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(4\) over \(\Q(\zeta_{5})\)
Coefficient field: 16.0.273503893564697265625.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} - 3 x^{15} + 7 x^{14} - 9 x^{13} + 19 x^{12} - 16 x^{11} + 49 x^{10} - 32 x^{9} + 98 x^{8} - 110 x^{7} + 145 x^{6} - 40 x^{5} + 52 x^{4} + 24 x^{3} + 19 x^{2} + 6 x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 92.1
Root \(-0.132595 + 0.408085i\) of defining polynomial
Character \(\chi\) \(=\) 143.92
Dual form 143.2.h.b.14.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.03831 - 0.754373i) q^{2} +(0.598926 - 1.84330i) q^{3} +(-0.109035 - 0.335575i) q^{4} +(2.14189 - 1.55618i) q^{5} +(-2.01241 + 1.46210i) q^{6} +(0.230284 + 0.708742i) q^{7} +(-0.933132 + 2.87188i) q^{8} +(-0.612005 - 0.444648i) q^{9} +O(q^{10})\) \(q+(-1.03831 - 0.754373i) q^{2} +(0.598926 - 1.84330i) q^{3} +(-0.109035 - 0.335575i) q^{4} +(2.14189 - 1.55618i) q^{5} +(-2.01241 + 1.46210i) q^{6} +(0.230284 + 0.708742i) q^{7} +(-0.933132 + 2.87188i) q^{8} +(-0.612005 - 0.444648i) q^{9} -3.39787 q^{10} +(-3.17179 - 0.969420i) q^{11} -0.683870 q^{12} +(0.809017 + 0.587785i) q^{13} +(0.295551 - 0.909611i) q^{14} +(-1.58567 - 4.88019i) q^{15} +(2.56443 - 1.86317i) q^{16} +(2.09280 - 1.52051i) q^{17} +(0.300018 + 0.923360i) q^{18} +(-1.34601 + 4.14260i) q^{19} +(-0.755754 - 0.549088i) q^{20} +1.44435 q^{21} +(2.56198 + 3.39926i) q^{22} -2.54998 q^{23} +(4.73488 + 3.44009i) q^{24} +(0.620934 - 1.91104i) q^{25} +(-0.396597 - 1.22060i) q^{26} +(3.51786 - 2.55587i) q^{27} +(0.212727 - 0.154555i) q^{28} +(-0.593075 - 1.82530i) q^{29} +(-2.03507 + 6.26331i) q^{30} +(4.92311 + 3.57685i) q^{31} +1.97117 q^{32} +(-3.68660 + 5.26595i) q^{33} -3.31999 q^{34} +(1.59617 + 1.15969i) q^{35} +(-0.0824827 + 0.253856i) q^{36} +(2.68248 + 8.25583i) q^{37} +(4.52264 - 3.28589i) q^{38} +(1.56801 - 1.13922i) q^{39} +(2.47049 + 7.60338i) q^{40} +(3.11180 - 9.57715i) q^{41} +(-1.49968 - 1.08958i) q^{42} -0.689106 q^{43} +(0.0205222 + 1.17007i) q^{44} -2.00280 q^{45} +(2.64765 + 1.92363i) q^{46} +(-1.99298 + 6.13377i) q^{47} +(-1.89848 - 5.84293i) q^{48} +(5.21383 - 3.78807i) q^{49} +(-2.08635 + 1.51582i) q^{50} +(-1.54933 - 4.76833i) q^{51} +(0.109035 - 0.335575i) q^{52} +(-5.94896 - 4.32217i) q^{53} -5.58069 q^{54} +(-8.30221 + 2.85946i) q^{55} -2.25031 q^{56} +(6.82992 + 4.96222i) q^{57} +(-0.761161 + 2.34261i) q^{58} +(-0.377050 - 1.16044i) q^{59} +(-1.46478 + 1.06422i) q^{60} +(1.52798 - 1.11014i) q^{61} +(-2.41341 - 7.42772i) q^{62} +(0.174206 - 0.536149i) q^{63} +(-7.17554 - 5.21333i) q^{64} +2.64752 q^{65} +(7.80031 - 2.68660i) q^{66} -11.2120 q^{67} +(-0.738432 - 0.536502i) q^{68} +(-1.52725 + 4.70038i) q^{69} +(-0.782477 - 2.40822i) q^{70} +(11.2126 - 8.14640i) q^{71} +(1.84806 - 1.34269i) q^{72} +(3.90819 + 12.0282i) q^{73} +(3.44274 - 10.5957i) q^{74} +(-3.15073 - 2.28914i) q^{75} +1.53692 q^{76} +(-0.0433435 - 2.47122i) q^{77} -2.48747 q^{78} +(-6.64308 - 4.82648i) q^{79} +(2.59332 - 7.98141i) q^{80} +(-3.30561 - 10.1736i) q^{81} +(-10.4557 + 7.59654i) q^{82} +(-12.4149 + 9.01996i) q^{83} +(-0.157485 - 0.484688i) q^{84} +(2.11637 - 6.51352i) q^{85} +(0.715503 + 0.519843i) q^{86} -3.71978 q^{87} +(5.74376 - 8.20440i) q^{88} -6.22197 q^{89} +(2.07952 + 1.51086i) q^{90} +(-0.230284 + 0.708742i) q^{91} +(0.278036 + 0.855708i) q^{92} +(9.54180 - 6.93252i) q^{93} +(6.69648 - 4.86528i) q^{94} +(3.56360 + 10.9676i) q^{95} +(1.18058 - 3.63346i) q^{96} +(2.97640 + 2.16248i) q^{97} -8.27117 q^{98} +(1.51010 + 2.00362i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + 2 q^{2} + 5 q^{3} - 8 q^{4} + 5 q^{5} - 4 q^{6} + 9 q^{7} - 4 q^{8} - 7 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q + 2 q^{2} + 5 q^{3} - 8 q^{4} + 5 q^{5} - 4 q^{6} + 9 q^{7} - 4 q^{8} - 7 q^{9} - 12 q^{10} + 6 q^{11} - 14 q^{12} + 4 q^{13} - q^{14} - 10 q^{15} + 10 q^{16} - 6 q^{17} + 20 q^{18} + 2 q^{19} - 21 q^{20} - 8 q^{21} + 2 q^{22} - 46 q^{23} + 3 q^{24} + 23 q^{25} + 3 q^{26} + 17 q^{27} - 9 q^{28} - 25 q^{29} + 22 q^{30} + 3 q^{31} + 24 q^{32} - 10 q^{33} + 4 q^{34} + 26 q^{35} - 2 q^{36} - 7 q^{37} + 5 q^{38} + 25 q^{40} - 3 q^{41} - 12 q^{42} - 16 q^{43} + 32 q^{44} - 46 q^{45} - 11 q^{46} + 13 q^{47} - 24 q^{48} + 19 q^{49} - 19 q^{50} - 23 q^{51} + 8 q^{52} - 14 q^{53} + 6 q^{54} - 5 q^{55} - 68 q^{56} + 23 q^{57} + 20 q^{58} + 16 q^{59} + 34 q^{60} - 13 q^{61} + 28 q^{62} + 18 q^{63} - 40 q^{64} + 10 q^{65} + 41 q^{66} - 62 q^{67} + 13 q^{68} + 4 q^{69} - 2 q^{70} + 54 q^{71} + 21 q^{72} - 42 q^{73} + 42 q^{74} + 51 q^{75} - 4 q^{76} + 14 q^{77} - 6 q^{78} - 15 q^{79} - 19 q^{80} + q^{81} - 7 q^{82} - 43 q^{83} - 35 q^{84} - 3 q^{85} - 32 q^{86} + 4 q^{87} + 41 q^{88} - 30 q^{89} + 26 q^{90} - 9 q^{91} + 3 q^{92} + 49 q^{93} + 4 q^{94} + 23 q^{95} + 23 q^{96} - 12 q^{97} + 24 q^{98} - 7 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/143\mathbb{Z}\right)^\times\).

\(n\) \(67\) \(79\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{5}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.03831 0.754373i −0.734193 0.533422i 0.156694 0.987647i \(-0.449916\pi\)
−0.890887 + 0.454225i \(0.849916\pi\)
\(3\) 0.598926 1.84330i 0.345790 1.06423i −0.615370 0.788239i \(-0.710993\pi\)
0.961160 0.275993i \(-0.0890067\pi\)
\(4\) −0.109035 0.335575i −0.0545174 0.167787i
\(5\) 2.14189 1.55618i 0.957883 0.695943i 0.00522508 0.999986i \(-0.498337\pi\)
0.952658 + 0.304043i \(0.0983368\pi\)
\(6\) −2.01241 + 1.46210i −0.821561 + 0.596899i
\(7\) 0.230284 + 0.708742i 0.0870393 + 0.267879i 0.985097 0.171997i \(-0.0550221\pi\)
−0.898058 + 0.439877i \(0.855022\pi\)
\(8\) −0.933132 + 2.87188i −0.329912 + 1.01536i
\(9\) −0.612005 0.444648i −0.204002 0.148216i
\(10\) −3.39787 −1.07450
\(11\) −3.17179 0.969420i −0.956329 0.292291i
\(12\) −0.683870 −0.197416
\(13\) 0.809017 + 0.587785i 0.224381 + 0.163022i
\(14\) 0.295551 0.909611i 0.0789892 0.243104i
\(15\) −1.58567 4.88019i −0.409418 1.26006i
\(16\) 2.56443 1.86317i 0.641108 0.465792i
\(17\) 2.09280 1.52051i 0.507578 0.368777i −0.304326 0.952568i \(-0.598431\pi\)
0.811904 + 0.583791i \(0.198431\pi\)
\(18\) 0.300018 + 0.923360i 0.0707149 + 0.217638i
\(19\) −1.34601 + 4.14260i −0.308797 + 0.950379i 0.669436 + 0.742869i \(0.266536\pi\)
−0.978233 + 0.207509i \(0.933464\pi\)
\(20\) −0.755754 0.549088i −0.168992 0.122780i
\(21\) 1.44435 0.315183
\(22\) 2.56198 + 3.39926i 0.546215 + 0.724725i
\(23\) −2.54998 −0.531707 −0.265853 0.964014i \(-0.585654\pi\)
−0.265853 + 0.964014i \(0.585654\pi\)
\(24\) 4.73488 + 3.44009i 0.966503 + 0.702205i
\(25\) 0.620934 1.91104i 0.124187 0.382208i
\(26\) −0.396597 1.22060i −0.0777791 0.239380i
\(27\) 3.51786 2.55587i 0.677012 0.491878i
\(28\) 0.212727 0.154555i 0.0402016 0.0292082i
\(29\) −0.593075 1.82530i −0.110131 0.338949i 0.880769 0.473546i \(-0.157026\pi\)
−0.990900 + 0.134597i \(0.957026\pi\)
\(30\) −2.03507 + 6.26331i −0.371552 + 1.14352i
\(31\) 4.92311 + 3.57685i 0.884217 + 0.642421i 0.934364 0.356321i \(-0.115969\pi\)
−0.0501470 + 0.998742i \(0.515969\pi\)
\(32\) 1.97117 0.348457
\(33\) −3.68660 + 5.26595i −0.641755 + 0.916685i
\(34\) −3.31999 −0.569374
\(35\) 1.59617 + 1.15969i 0.269802 + 0.196023i
\(36\) −0.0824827 + 0.253856i −0.0137471 + 0.0423093i
\(37\) 2.68248 + 8.25583i 0.440997 + 1.35725i 0.886814 + 0.462126i \(0.152913\pi\)
−0.445817 + 0.895124i \(0.647087\pi\)
\(38\) 4.52264 3.28589i 0.733669 0.533042i
\(39\) 1.56801 1.13922i 0.251082 0.182422i
\(40\) 2.47049 + 7.60338i 0.390619 + 1.20220i
\(41\) 3.11180 9.57715i 0.485982 1.49570i −0.344571 0.938760i \(-0.611976\pi\)
0.830554 0.556939i \(-0.188024\pi\)
\(42\) −1.49968 1.08958i −0.231405 0.168126i
\(43\) −0.689106 −0.105088 −0.0525439 0.998619i \(-0.516733\pi\)
−0.0525439 + 0.998619i \(0.516733\pi\)
\(44\) 0.0205222 + 1.17007i 0.00309385 + 0.176395i
\(45\) −2.00280 −0.298560
\(46\) 2.64765 + 1.92363i 0.390375 + 0.283624i
\(47\) −1.99298 + 6.13377i −0.290707 + 0.894703i 0.693923 + 0.720049i \(0.255881\pi\)
−0.984630 + 0.174654i \(0.944119\pi\)
\(48\) −1.89848 5.84293i −0.274022 0.843354i
\(49\) 5.21383 3.78807i 0.744833 0.541153i
\(50\) −2.08635 + 1.51582i −0.295055 + 0.214370i
\(51\) −1.54933 4.76833i −0.216949 0.667700i
\(52\) 0.109035 0.335575i 0.0151204 0.0465359i
\(53\) −5.94896 4.32217i −0.817152 0.593696i 0.0987430 0.995113i \(-0.468518\pi\)
−0.915895 + 0.401417i \(0.868518\pi\)
\(54\) −5.58069 −0.759436
\(55\) −8.30221 + 2.85946i −1.11947 + 0.385570i
\(56\) −2.25031 −0.300710
\(57\) 6.82992 + 4.96222i 0.904644 + 0.657263i
\(58\) −0.761161 + 2.34261i −0.0999454 + 0.307600i
\(59\) −0.377050 1.16044i −0.0490878 0.151077i 0.923508 0.383579i \(-0.125309\pi\)
−0.972596 + 0.232502i \(0.925309\pi\)
\(60\) −1.46478 + 1.06422i −0.189102 + 0.137390i
\(61\) 1.52798 1.11014i 0.195638 0.142139i −0.485654 0.874151i \(-0.661418\pi\)
0.681292 + 0.732012i \(0.261418\pi\)
\(62\) −2.41341 7.42772i −0.306504 0.943322i
\(63\) 0.174206 0.536149i 0.0219478 0.0675485i
\(64\) −7.17554 5.21333i −0.896942 0.651667i
\(65\) 2.64752 0.328385
\(66\) 7.80031 2.68660i 0.960151 0.330697i
\(67\) −11.2120 −1.36977 −0.684883 0.728653i \(-0.740147\pi\)
−0.684883 + 0.728653i \(0.740147\pi\)
\(68\) −0.738432 0.536502i −0.0895480 0.0650604i
\(69\) −1.52725 + 4.70038i −0.183859 + 0.565859i
\(70\) −0.782477 2.40822i −0.0935239 0.287837i
\(71\) 11.2126 8.14640i 1.33069 0.966799i 0.330953 0.943647i \(-0.392630\pi\)
0.999732 0.0231522i \(-0.00737022\pi\)
\(72\) 1.84806 1.34269i 0.217796 0.158238i
\(73\) 3.90819 + 12.0282i 0.457419 + 1.40779i 0.868272 + 0.496088i \(0.165231\pi\)
−0.410854 + 0.911701i \(0.634769\pi\)
\(74\) 3.44274 10.5957i 0.400210 1.23172i
\(75\) −3.15073 2.28914i −0.363815 0.264327i
\(76\) 1.53692 0.176296
\(77\) −0.0433435 2.47122i −0.00493945 0.281622i
\(78\) −2.48747 −0.281651
\(79\) −6.64308 4.82648i −0.747405 0.543022i 0.147616 0.989045i \(-0.452840\pi\)
−0.895022 + 0.446023i \(0.852840\pi\)
\(80\) 2.59332 7.98141i 0.289942 0.892349i
\(81\) −3.30561 10.1736i −0.367290 1.13040i
\(82\) −10.4557 + 7.59654i −1.15464 + 0.838897i
\(83\) −12.4149 + 9.01996i −1.36271 + 0.990069i −0.364446 + 0.931224i \(0.618742\pi\)
−0.998267 + 0.0588448i \(0.981258\pi\)
\(84\) −0.157485 0.484688i −0.0171830 0.0528838i
\(85\) 2.11637 6.51352i 0.229553 0.706491i
\(86\) 0.715503 + 0.519843i 0.0771546 + 0.0560561i
\(87\) −3.71978 −0.398803
\(88\) 5.74376 8.20440i 0.612286 0.874592i
\(89\) −6.22197 −0.659527 −0.329764 0.944064i \(-0.606969\pi\)
−0.329764 + 0.944064i \(0.606969\pi\)
\(90\) 2.07952 + 1.51086i 0.219200 + 0.159258i
\(91\) −0.230284 + 0.708742i −0.0241404 + 0.0742964i
\(92\) 0.278036 + 0.855708i 0.0289873 + 0.0892137i
\(93\) 9.54180 6.93252i 0.989438 0.718869i
\(94\) 6.69648 4.86528i 0.690689 0.501815i
\(95\) 3.56360 + 10.9676i 0.365618 + 1.12526i
\(96\) 1.18058 3.63346i 0.120493 0.370839i
\(97\) 2.97640 + 2.16248i 0.302207 + 0.219566i 0.728546 0.684997i \(-0.240197\pi\)
−0.426338 + 0.904564i \(0.640197\pi\)
\(98\) −8.27117 −0.835514
\(99\) 1.51010 + 2.00362i 0.151771 + 0.201371i
\(100\) −0.709000 −0.0709000
\(101\) 6.42016 + 4.66452i 0.638830 + 0.464137i 0.859448 0.511223i \(-0.170808\pi\)
−0.220618 + 0.975360i \(0.570808\pi\)
\(102\) −1.98843 + 6.11975i −0.196884 + 0.605946i
\(103\) 3.36871 + 10.3678i 0.331929 + 1.02157i 0.968215 + 0.250119i \(0.0804697\pi\)
−0.636286 + 0.771453i \(0.719530\pi\)
\(104\) −2.44297 + 1.77492i −0.239553 + 0.174045i
\(105\) 3.09364 2.24766i 0.301909 0.219349i
\(106\) 2.91631 + 8.97547i 0.283257 + 0.871774i
\(107\) −3.13233 + 9.64033i −0.302814 + 0.931966i 0.677670 + 0.735367i \(0.262990\pi\)
−0.980484 + 0.196600i \(0.937010\pi\)
\(108\) −1.24126 0.901825i −0.119440 0.0867782i
\(109\) −13.6830 −1.31059 −0.655296 0.755372i \(-0.727456\pi\)
−0.655296 + 0.755372i \(0.727456\pi\)
\(110\) 10.7773 + 3.29397i 1.02758 + 0.314067i
\(111\) 16.8246 1.59692
\(112\) 1.91106 + 1.38846i 0.180578 + 0.131197i
\(113\) −4.95050 + 15.2361i −0.465704 + 1.43329i 0.392391 + 0.919799i \(0.371648\pi\)
−0.858095 + 0.513491i \(0.828352\pi\)
\(114\) −3.34817 10.3046i −0.313585 0.965115i
\(115\) −5.46177 + 3.96821i −0.509313 + 0.370037i
\(116\) −0.547858 + 0.398042i −0.0508673 + 0.0369573i
\(117\) −0.233765 0.719455i −0.0216116 0.0665137i
\(118\) −0.483912 + 1.48933i −0.0445477 + 0.137104i
\(119\) 1.55959 + 1.13311i 0.142967 + 0.103872i
\(120\) 15.4950 1.41449
\(121\) 9.12045 + 6.14959i 0.829132 + 0.559053i
\(122\) −2.42398 −0.219456
\(123\) −15.7898 11.4720i −1.42372 1.03440i
\(124\) 0.663510 2.04207i 0.0595849 0.183384i
\(125\) 2.44671 + 7.53021i 0.218841 + 0.673522i
\(126\) −0.585335 + 0.425271i −0.0521458 + 0.0378861i
\(127\) 8.38956 6.09537i 0.744453 0.540877i −0.149650 0.988739i \(-0.547815\pi\)
0.894102 + 0.447863i \(0.147815\pi\)
\(128\) 2.29935 + 7.07668i 0.203236 + 0.625496i
\(129\) −0.412724 + 1.27023i −0.0363383 + 0.111838i
\(130\) −2.74894 1.99722i −0.241098 0.175168i
\(131\) −5.95780 −0.520535 −0.260268 0.965536i \(-0.583811\pi\)
−0.260268 + 0.965536i \(0.583811\pi\)
\(132\) 2.16909 + 0.662958i 0.188795 + 0.0577030i
\(133\) −3.24600 −0.281464
\(134\) 11.6415 + 8.45804i 1.00567 + 0.730663i
\(135\) 3.55748 10.9488i 0.306179 0.942323i
\(136\) 2.41386 + 7.42911i 0.206987 + 0.637041i
\(137\) 3.84423 2.79300i 0.328435 0.238622i −0.411331 0.911486i \(-0.634936\pi\)
0.739766 + 0.672864i \(0.234936\pi\)
\(138\) 5.13158 3.72831i 0.436829 0.317375i
\(139\) 0.847346 + 2.60786i 0.0718709 + 0.221196i 0.980539 0.196322i \(-0.0628999\pi\)
−0.908668 + 0.417518i \(0.862900\pi\)
\(140\) 0.215123 0.662081i 0.0181812 0.0559561i
\(141\) 10.1128 + 7.34735i 0.851648 + 0.618758i
\(142\) −17.7875 −1.49269
\(143\) −1.99622 2.64861i −0.166932 0.221488i
\(144\) −2.39790 −0.199825
\(145\) −4.11078 2.98666i −0.341382 0.248029i
\(146\) 5.01583 15.4371i 0.415113 1.27759i
\(147\) −3.85987 11.8795i −0.318357 0.979801i
\(148\) 2.47797 1.80035i 0.203688 0.147988i
\(149\) −12.5869 + 9.14492i −1.03116 + 0.749181i −0.968540 0.248857i \(-0.919945\pi\)
−0.0626184 + 0.998038i \(0.519945\pi\)
\(150\) 1.54455 + 4.75365i 0.126112 + 0.388134i
\(151\) 5.75835 17.7224i 0.468608 1.44223i −0.385779 0.922591i \(-0.626067\pi\)
0.854387 0.519636i \(-0.173933\pi\)
\(152\) −10.6411 7.73119i −0.863105 0.627082i
\(153\) −1.95689 −0.158205
\(154\) −1.81922 + 2.59858i −0.146597 + 0.209399i
\(155\) 16.1110 1.29406
\(156\) −0.553263 0.401969i −0.0442965 0.0321833i
\(157\) 4.76704 14.6714i 0.380451 1.17091i −0.559276 0.828982i \(-0.688921\pi\)
0.939727 0.341926i \(-0.111079\pi\)
\(158\) 3.25658 + 10.0227i 0.259080 + 0.797365i
\(159\) −11.5301 + 8.37708i −0.914393 + 0.664346i
\(160\) 4.22203 3.06748i 0.333781 0.242506i
\(161\) −0.587219 1.80728i −0.0462794 0.142433i
\(162\) −4.24247 + 13.0570i −0.333320 + 1.02585i
\(163\) −7.27740 5.28734i −0.570010 0.414137i 0.265099 0.964221i \(-0.414595\pi\)
−0.835109 + 0.550085i \(0.814595\pi\)
\(164\) −3.55314 −0.277454
\(165\) 0.298450 + 17.0161i 0.0232343 + 1.32470i
\(166\) 19.6949 1.52862
\(167\) −10.4945 7.62473i −0.812092 0.590020i 0.102344 0.994749i \(-0.467366\pi\)
−0.914436 + 0.404730i \(0.867366\pi\)
\(168\) −1.34777 + 4.14801i −0.103983 + 0.320026i
\(169\) 0.309017 + 0.951057i 0.0237705 + 0.0731582i
\(170\) −7.11106 + 5.16649i −0.545394 + 0.396252i
\(171\) 2.66577 1.93679i 0.203856 0.148110i
\(172\) 0.0751366 + 0.231247i 0.00572912 + 0.0176324i
\(173\) −0.0822824 + 0.253239i −0.00625582 + 0.0192534i −0.954136 0.299374i \(-0.903222\pi\)
0.947880 + 0.318628i \(0.103222\pi\)
\(174\) 3.86227 + 2.80610i 0.292798 + 0.212730i
\(175\) 1.49742 0.113195
\(176\) −9.94002 + 3.42356i −0.749257 + 0.258061i
\(177\) −2.36487 −0.177755
\(178\) 6.46030 + 4.69368i 0.484220 + 0.351806i
\(179\) −4.77816 + 14.7057i −0.357136 + 1.09915i 0.597624 + 0.801776i \(0.296111\pi\)
−0.954760 + 0.297376i \(0.903889\pi\)
\(180\) 0.218375 + 0.672089i 0.0162767 + 0.0500946i
\(181\) −11.5005 + 8.35558i −0.854823 + 0.621065i −0.926472 0.376365i \(-0.877174\pi\)
0.0716488 + 0.997430i \(0.477174\pi\)
\(182\) 0.773761 0.562170i 0.0573550 0.0416708i
\(183\) −1.13119 3.48143i −0.0836197 0.257355i
\(184\) 2.37946 7.32323i 0.175416 0.539876i
\(185\) 18.5931 + 13.5087i 1.36699 + 0.993179i
\(186\) −15.1370 −1.10990
\(187\) −8.11192 + 2.79392i −0.593202 + 0.204312i
\(188\) 2.27565 0.165969
\(189\) 2.62156 + 1.90468i 0.190691 + 0.138545i
\(190\) 4.57359 14.0760i 0.331803 1.02118i
\(191\) −5.00983 15.4187i −0.362499 1.11566i −0.951533 0.307548i \(-0.900491\pi\)
0.589034 0.808108i \(-0.299509\pi\)
\(192\) −13.9074 + 10.1043i −1.00368 + 0.729215i
\(193\) −9.07265 + 6.59167i −0.653064 + 0.474479i −0.864313 0.502954i \(-0.832247\pi\)
0.211250 + 0.977432i \(0.432247\pi\)
\(194\) −1.45909 4.49062i −0.104757 0.322408i
\(195\) 1.58567 4.88019i 0.113552 0.349478i
\(196\) −1.83967 1.33660i −0.131405 0.0954714i
\(197\) 15.8589 1.12990 0.564948 0.825126i \(-0.308896\pi\)
0.564948 + 0.825126i \(0.308896\pi\)
\(198\) −0.0564685 3.21954i −0.00401304 0.228803i
\(199\) 7.12728 0.505239 0.252620 0.967566i \(-0.418708\pi\)
0.252620 + 0.967566i \(0.418708\pi\)
\(200\) 4.90887 + 3.56650i 0.347109 + 0.252190i
\(201\) −6.71516 + 20.6671i −0.473651 + 1.45775i
\(202\) −3.14730 9.68638i −0.221443 0.681532i
\(203\) 1.15709 0.840674i 0.0812117 0.0590038i
\(204\) −1.43120 + 1.03983i −0.100204 + 0.0728026i
\(205\) −8.23857 25.3557i −0.575407 1.77092i
\(206\) 4.32345 13.3062i 0.301229 0.927089i
\(207\) 1.56060 + 1.13384i 0.108469 + 0.0788074i
\(208\) 3.16981 0.219787
\(209\) 8.28519 11.8346i 0.573099 0.818616i
\(210\) −4.90772 −0.338665
\(211\) −13.8212 10.0417i −0.951494 0.691301i −0.000334297 1.00000i \(-0.500106\pi\)
−0.951160 + 0.308699i \(0.900106\pi\)
\(212\) −0.801768 + 2.46759i −0.0550657 + 0.169475i
\(213\) −8.30080 25.5472i −0.568761 1.75047i
\(214\) 10.5247 7.64666i 0.719455 0.522715i
\(215\) −1.47599 + 1.07237i −0.100662 + 0.0731351i
\(216\) 4.05755 + 12.4878i 0.276081 + 0.849690i
\(217\) −1.40135 + 4.31291i −0.0951298 + 0.292779i
\(218\) 14.2071 + 10.3221i 0.962227 + 0.699099i
\(219\) 24.5123 1.65639
\(220\) 1.86479 + 2.47423i 0.125724 + 0.166813i
\(221\) 2.58684 0.174010
\(222\) −17.4691 12.6920i −1.17245 0.851833i
\(223\) 1.67632 5.15917i 0.112254 0.345484i −0.879110 0.476619i \(-0.841862\pi\)
0.991365 + 0.131135i \(0.0418622\pi\)
\(224\) 0.453929 + 1.39705i 0.0303294 + 0.0933443i
\(225\) −1.22975 + 0.893468i −0.0819836 + 0.0595646i
\(226\) 16.6338 12.0852i 1.10647 0.803894i
\(227\) −8.60379 26.4798i −0.571054 1.75752i −0.649239 0.760584i \(-0.724913\pi\)
0.0781852 0.996939i \(-0.475087\pi\)
\(228\) 0.920499 2.83300i 0.0609615 0.187620i
\(229\) −9.93587 7.21883i −0.656581 0.477034i 0.208926 0.977932i \(-0.433003\pi\)
−0.865507 + 0.500898i \(0.833003\pi\)
\(230\) 8.66449 0.571320
\(231\) −4.58117 1.40018i −0.301419 0.0921252i
\(232\) 5.79546 0.380490
\(233\) 4.16123 + 3.02331i 0.272611 + 0.198064i 0.715688 0.698420i \(-0.246113\pi\)
−0.443077 + 0.896484i \(0.646113\pi\)
\(234\) −0.300018 + 0.923360i −0.0196128 + 0.0603619i
\(235\) 5.27647 + 16.2393i 0.344199 + 1.05934i
\(236\) −0.348303 + 0.253057i −0.0226726 + 0.0164726i
\(237\) −12.8754 + 9.35452i −0.836346 + 0.607641i
\(238\) −0.764542 2.35302i −0.0495579 0.152524i
\(239\) −5.30051 + 16.3133i −0.342862 + 1.05522i 0.619857 + 0.784715i \(0.287191\pi\)
−0.962719 + 0.270505i \(0.912809\pi\)
\(240\) −13.1590 9.56055i −0.849407 0.617131i
\(241\) 8.51862 0.548733 0.274366 0.961625i \(-0.411532\pi\)
0.274366 + 0.961625i \(0.411532\pi\)
\(242\) −4.83073 13.2654i −0.310531 0.852730i
\(243\) −7.68796 −0.493183
\(244\) −0.539140 0.391708i −0.0345149 0.0250766i
\(245\) 5.27256 16.2273i 0.336852 1.03672i
\(246\) 7.74052 + 23.8229i 0.493517 + 1.51889i
\(247\) −3.52391 + 2.56027i −0.224221 + 0.162906i
\(248\) −14.8662 + 10.8009i −0.944005 + 0.685860i
\(249\) 9.19092 + 28.2867i 0.582451 + 1.79260i
\(250\) 3.14015 9.66438i 0.198600 0.611229i
\(251\) 16.9379 + 12.3061i 1.06911 + 0.776756i 0.975753 0.218877i \(-0.0702392\pi\)
0.0933601 + 0.995632i \(0.470239\pi\)
\(252\) −0.198913 −0.0125303
\(253\) 8.08797 + 2.47200i 0.508487 + 0.155413i
\(254\) −13.3091 −0.835087
\(255\) −10.7389 7.80223i −0.672493 0.488595i
\(256\) −2.53060 + 7.78838i −0.158162 + 0.486774i
\(257\) 2.52391 + 7.76780i 0.157437 + 0.484542i 0.998400 0.0565514i \(-0.0180105\pi\)
−0.840962 + 0.541094i \(0.818010\pi\)
\(258\) 1.38676 1.00754i 0.0863360 0.0627268i
\(259\) −5.23352 + 3.80238i −0.325195 + 0.236268i
\(260\) −0.288672 0.888443i −0.0179027 0.0550989i
\(261\) −0.448649 + 1.38080i −0.0277707 + 0.0854694i
\(262\) 6.18601 + 4.49440i 0.382173 + 0.277665i
\(263\) 17.8103 1.09823 0.549115 0.835747i \(-0.314965\pi\)
0.549115 + 0.835747i \(0.314965\pi\)
\(264\) −11.6831 15.5013i −0.719047 0.954040i
\(265\) −19.4681 −1.19592
\(266\) 3.37034 + 2.44870i 0.206649 + 0.150139i
\(267\) −3.72650 + 11.4690i −0.228058 + 0.701890i
\(268\) 1.22250 + 3.76247i 0.0746761 + 0.229829i
\(269\) 23.6906 17.2123i 1.44444 1.04945i 0.457353 0.889285i \(-0.348798\pi\)
0.987090 0.160164i \(-0.0512024\pi\)
\(270\) −11.9532 + 8.68453i −0.727451 + 0.528524i
\(271\) −7.45600 22.9472i −0.452920 1.39394i −0.873560 0.486716i \(-0.838195\pi\)
0.420641 0.907227i \(-0.361805\pi\)
\(272\) 2.53388 7.79847i 0.153639 0.472852i
\(273\) 1.16850 + 0.848968i 0.0707211 + 0.0513819i
\(274\) −6.09844 −0.368420
\(275\) −3.82207 + 5.45946i −0.230479 + 0.329218i
\(276\) 1.74385 0.104968
\(277\) 3.74192 + 2.71867i 0.224830 + 0.163349i 0.694498 0.719494i \(-0.255626\pi\)
−0.469668 + 0.882843i \(0.655626\pi\)
\(278\) 1.08750 3.34697i 0.0652237 0.200738i
\(279\) −1.42253 4.37810i −0.0851647 0.262110i
\(280\) −4.81992 + 3.50188i −0.288046 + 0.209277i
\(281\) −6.23511 + 4.53007i −0.371955 + 0.270241i −0.758021 0.652230i \(-0.773834\pi\)
0.386066 + 0.922471i \(0.373834\pi\)
\(282\) −4.95749 15.2576i −0.295214 0.908576i
\(283\) −5.70086 + 17.5454i −0.338881 + 1.04297i 0.625897 + 0.779905i \(0.284733\pi\)
−0.964779 + 0.263063i \(0.915267\pi\)
\(284\) −3.95629 2.87441i −0.234762 0.170565i
\(285\) 22.3510 1.32396
\(286\) 0.0746464 + 4.25595i 0.00441394 + 0.251660i
\(287\) 7.50433 0.442966
\(288\) −1.20636 0.876475i −0.0710857 0.0516468i
\(289\) −3.18543 + 9.80373i −0.187378 + 0.576690i
\(290\) 2.01519 + 6.20213i 0.118336 + 0.364201i
\(291\) 5.76874 4.19124i 0.338170 0.245695i
\(292\) 3.61022 2.62298i 0.211272 0.153498i
\(293\) −7.19342 22.1391i −0.420244 1.29338i −0.907475 0.420106i \(-0.861993\pi\)
0.487231 0.873273i \(-0.338007\pi\)
\(294\) −4.95382 + 15.2463i −0.288912 + 0.889181i
\(295\) −2.61345 1.89878i −0.152161 0.110551i
\(296\) −26.2129 −1.52359
\(297\) −13.6356 + 4.69640i −0.791218 + 0.272513i
\(298\) 19.9677 1.15670
\(299\) −2.06297 1.49884i −0.119305 0.0866800i
\(300\) −0.424638 + 1.30690i −0.0245165 + 0.0754540i
\(301\) −0.158690 0.488399i −0.00914676 0.0281508i
\(302\) −19.3482 + 14.0573i −1.11336 + 0.808907i
\(303\) 12.4433 9.04060i 0.714850 0.519369i
\(304\) 4.26661 + 13.1313i 0.244707 + 0.753130i
\(305\) 1.54520 4.75562i 0.0884776 0.272306i
\(306\) 2.03185 + 1.47623i 0.116153 + 0.0843903i
\(307\) 10.0454 0.573324 0.286662 0.958032i \(-0.407454\pi\)
0.286662 + 0.958032i \(0.407454\pi\)
\(308\) −0.824554 + 0.283994i −0.0469833 + 0.0161821i
\(309\) 21.1286 1.20197
\(310\) −16.7281 12.1537i −0.950093 0.690283i
\(311\) −1.07355 + 3.30406i −0.0608756 + 0.187356i −0.976869 0.213836i \(-0.931404\pi\)
0.915994 + 0.401192i \(0.131404\pi\)
\(312\) 1.80856 + 5.56618i 0.102390 + 0.315123i
\(313\) 9.71731 7.06004i 0.549255 0.399057i −0.278256 0.960507i \(-0.589756\pi\)
0.827511 + 0.561450i \(0.189756\pi\)
\(314\) −16.0174 + 11.6373i −0.903913 + 0.656731i
\(315\) −0.461213 1.41947i −0.0259864 0.0799780i
\(316\) −0.895319 + 2.75551i −0.0503656 + 0.155009i
\(317\) 8.93176 + 6.48930i 0.501658 + 0.364476i 0.809650 0.586913i \(-0.199657\pi\)
−0.307992 + 0.951389i \(0.599657\pi\)
\(318\) 18.2912 1.02572
\(319\) 0.111627 + 6.36439i 0.00624991 + 0.356337i
\(320\) −23.4821 −1.31269
\(321\) 15.8940 + 11.5477i 0.887118 + 0.644529i
\(322\) −0.753646 + 2.31949i −0.0419991 + 0.129260i
\(323\) 3.48192 + 10.7163i 0.193739 + 0.596268i
\(324\) −3.05358 + 2.21856i −0.169644 + 0.123253i
\(325\) 1.62563 1.18109i 0.0901735 0.0655149i
\(326\) 3.56754 + 10.9798i 0.197588 + 0.608112i
\(327\) −8.19509 + 25.2219i −0.453190 + 1.39477i
\(328\) 24.6007 + 17.8735i 1.35835 + 0.986898i
\(329\) −4.80622 −0.264975
\(330\) 12.5266 17.8930i 0.689567 0.984980i
\(331\) 14.7379 0.810071 0.405035 0.914301i \(-0.367259\pi\)
0.405035 + 0.914301i \(0.367259\pi\)
\(332\) 4.38053 + 3.18264i 0.240413 + 0.174670i
\(333\) 2.02924 6.24537i 0.111202 0.342244i
\(334\) 5.14465 + 15.8336i 0.281503 + 0.866376i
\(335\) −24.0149 + 17.4479i −1.31208 + 0.953278i
\(336\) 3.70394 2.69107i 0.202066 0.146810i
\(337\) −8.65051 26.6235i −0.471224 1.45028i −0.850984 0.525192i \(-0.823994\pi\)
0.379760 0.925085i \(-0.376006\pi\)
\(338\) 0.396597 1.22060i 0.0215720 0.0663919i
\(339\) 25.1197 + 18.2506i 1.36432 + 0.991234i
\(340\) −2.41653 −0.131055
\(341\) −12.1476 16.1176i −0.657828 0.872815i
\(342\) −4.22894 −0.228675
\(343\) 8.10568 + 5.88912i 0.437665 + 0.317983i
\(344\) 0.643027 1.97903i 0.0346697 0.106702i
\(345\) 4.04342 + 12.4444i 0.217690 + 0.669982i
\(346\) 0.276471 0.200868i 0.0148632 0.0107987i
\(347\) 15.3441 11.1481i 0.823714 0.598463i −0.0940603 0.995567i \(-0.529985\pi\)
0.917774 + 0.397104i \(0.129985\pi\)
\(348\) 0.405586 + 1.24827i 0.0217417 + 0.0669141i
\(349\) 0.574029 1.76668i 0.0307271 0.0945681i −0.934517 0.355919i \(-0.884168\pi\)
0.965244 + 0.261351i \(0.0841679\pi\)
\(350\) −1.55478 1.12962i −0.0831067 0.0603805i
\(351\) 4.34831 0.232096
\(352\) −6.25212 1.91089i −0.333239 0.101851i
\(353\) −34.2457 −1.82272 −0.911358 0.411615i \(-0.864965\pi\)
−0.911358 + 0.411615i \(0.864965\pi\)
\(354\) 2.45546 + 1.78399i 0.130506 + 0.0948182i
\(355\) 11.3389 34.8974i 0.601804 1.85216i
\(356\) 0.678411 + 2.08794i 0.0359557 + 0.110660i
\(357\) 3.02273 2.19614i 0.159980 0.116232i
\(358\) 16.0547 11.6644i 0.848519 0.616485i
\(359\) 0.606925 + 1.86792i 0.0320323 + 0.0985852i 0.965794 0.259309i \(-0.0834948\pi\)
−0.933762 + 0.357894i \(0.883495\pi\)
\(360\) 1.86888 5.75181i 0.0984984 0.303147i
\(361\) 0.0219053 + 0.0159151i 0.00115291 + 0.000837639i
\(362\) 18.2442 0.958894
\(363\) 16.7980 13.1286i 0.881668 0.689073i
\(364\) 0.262945 0.0137821
\(365\) 27.0888 + 19.6812i 1.41789 + 1.03016i
\(366\) −1.45178 + 4.46812i −0.0758858 + 0.233553i
\(367\) 6.79332 + 20.9077i 0.354609 + 1.09137i 0.956236 + 0.292596i \(0.0945191\pi\)
−0.601628 + 0.798777i \(0.705481\pi\)
\(368\) −6.53924 + 4.75103i −0.340881 + 0.247665i
\(369\) −6.16290 + 4.47761i −0.320828 + 0.233095i
\(370\) −9.11474 28.0523i −0.473853 1.45837i
\(371\) 1.69335 5.21161i 0.0879146 0.270573i
\(372\) −3.36677 2.44610i −0.174559 0.126824i
\(373\) −13.3238 −0.689881 −0.344941 0.938624i \(-0.612101\pi\)
−0.344941 + 0.938624i \(0.612101\pi\)
\(374\) 10.5303 + 3.21847i 0.544509 + 0.166423i
\(375\) 15.3459 0.792457
\(376\) −15.7558 11.4472i −0.812542 0.590346i
\(377\) 0.593075 1.82530i 0.0305449 0.0940076i
\(378\) −1.28515 3.95527i −0.0661007 0.203437i
\(379\) 14.7529 10.7186i 0.757805 0.550577i −0.140431 0.990090i \(-0.544849\pi\)
0.898236 + 0.439513i \(0.144849\pi\)
\(380\) 3.29191 2.39171i 0.168871 0.122692i
\(381\) −6.21090 19.1152i −0.318194 0.979300i
\(382\) −6.42970 + 19.7886i −0.328972 + 1.01247i
\(383\) −13.4422 9.76635i −0.686866 0.499037i 0.188763 0.982023i \(-0.439552\pi\)
−0.875628 + 0.482986i \(0.839552\pi\)
\(384\) 14.4216 0.735949
\(385\) −3.93849 5.22564i −0.200724 0.266323i
\(386\) 14.3928 0.732572
\(387\) 0.421737 + 0.306410i 0.0214381 + 0.0155757i
\(388\) 0.401142 1.23459i 0.0203649 0.0626768i
\(389\) −10.9189 33.6049i −0.553609 1.70383i −0.699588 0.714547i \(-0.746633\pi\)
0.145978 0.989288i \(-0.453367\pi\)
\(390\) −5.32789 + 3.87094i −0.269788 + 0.196013i
\(391\) −5.33658 + 3.87725i −0.269883 + 0.196081i
\(392\) 6.01371 + 18.5083i 0.303738 + 0.934810i
\(393\) −3.56828 + 10.9820i −0.179996 + 0.553970i
\(394\) −16.4663 11.9635i −0.829562 0.602712i
\(395\) −21.7396 −1.09384
\(396\) 0.507710 0.725215i 0.0255134 0.0364434i
\(397\) −25.4379 −1.27669 −0.638345 0.769750i \(-0.720381\pi\)
−0.638345 + 0.769750i \(0.720381\pi\)
\(398\) −7.40029 5.37662i −0.370943 0.269506i
\(399\) −1.94412 + 5.98337i −0.0973275 + 0.299543i
\(400\) −1.96824 6.05763i −0.0984122 0.302882i
\(401\) −29.4272 + 21.3801i −1.46953 + 1.06767i −0.488774 + 0.872410i \(0.662556\pi\)
−0.980751 + 0.195262i \(0.937444\pi\)
\(402\) 22.5631 16.3931i 1.12535 0.817612i
\(403\) 1.88046 + 5.78746i 0.0936724 + 0.288294i
\(404\) 0.865274 2.66304i 0.0430490 0.132491i
\(405\) −22.9122 16.6467i −1.13852 0.827181i
\(406\) −1.83559 −0.0910990
\(407\) −0.504890 28.7862i −0.0250264 1.42688i
\(408\) 15.1398 0.749533
\(409\) −6.87898 4.99787i −0.340144 0.247129i 0.404579 0.914503i \(-0.367418\pi\)
−0.744723 + 0.667374i \(0.767418\pi\)
\(410\) −10.5735 + 32.5419i −0.522189 + 1.60713i
\(411\) −2.84593 8.75888i −0.140379 0.432044i
\(412\) 3.11187 2.26091i 0.153311 0.111387i
\(413\) 0.735625 0.534463i 0.0361977 0.0262992i
\(414\) −0.765038 2.35455i −0.0375996 0.115720i
\(415\) −12.5548 + 38.6396i −0.616289 + 1.89674i
\(416\) 1.59471 + 1.15862i 0.0781870 + 0.0568062i
\(417\) 5.31458 0.260256
\(418\) −17.5303 + 6.03780i −0.857433 + 0.295319i
\(419\) −15.9075 −0.777132 −0.388566 0.921421i \(-0.627029\pi\)
−0.388566 + 0.921421i \(0.627029\pi\)
\(420\) −1.09157 0.793075i −0.0532634 0.0386981i
\(421\) 10.7545 33.0991i 0.524145 1.61315i −0.241857 0.970312i \(-0.577756\pi\)
0.766001 0.642839i \(-0.222244\pi\)
\(422\) 6.77547 + 20.8527i 0.329825 + 1.01510i
\(423\) 3.94709 2.86773i 0.191914 0.139434i
\(424\) 17.9639 13.0516i 0.872406 0.633840i
\(425\) −1.60626 4.94355i −0.0779149 0.239797i
\(426\) −10.6534 + 32.7877i −0.516158 + 1.58857i
\(427\) 1.13868 + 0.827298i 0.0551045 + 0.0400357i
\(428\) 3.57659 0.172881
\(429\) −6.07777 + 2.09332i −0.293438 + 0.101066i
\(430\) 2.34150 0.112917
\(431\) 12.2973 + 8.93453i 0.592341 + 0.430361i 0.843152 0.537675i \(-0.180697\pi\)
−0.250811 + 0.968036i \(0.580697\pi\)
\(432\) 4.25928 13.1087i 0.204925 0.630694i
\(433\) −7.08150 21.7946i −0.340315 1.04738i −0.964044 0.265742i \(-0.914383\pi\)
0.623729 0.781641i \(-0.285617\pi\)
\(434\) 4.70857 3.42098i 0.226019 0.164212i
\(435\) −7.96737 + 5.78864i −0.382006 + 0.277544i
\(436\) 1.49192 + 4.59167i 0.0714501 + 0.219901i
\(437\) 3.43230 10.5635i 0.164189 0.505323i
\(438\) −25.4512 18.4914i −1.21611 0.883552i
\(439\) −5.35977 −0.255808 −0.127904 0.991787i \(-0.540825\pi\)
−0.127904 + 0.991787i \(0.540825\pi\)
\(440\) −0.464989 26.5112i −0.0221675 1.26387i
\(441\) −4.87525 −0.232155
\(442\) −2.68593 1.95144i −0.127757 0.0928206i
\(443\) −1.53432 + 4.72216i −0.0728978 + 0.224356i −0.980866 0.194682i \(-0.937633\pi\)
0.907969 + 0.419038i \(0.137633\pi\)
\(444\) −1.83447 5.64592i −0.0870601 0.267943i
\(445\) −13.3268 + 9.68247i −0.631750 + 0.458993i
\(446\) −5.63247 + 4.09223i −0.266705 + 0.193773i
\(447\) 9.31824 + 28.6786i 0.440738 + 1.35645i
\(448\) 2.04250 6.28616i 0.0964989 0.296993i
\(449\) −15.2981 11.1147i −0.721962 0.524536i 0.165048 0.986285i \(-0.447222\pi\)
−0.887010 + 0.461749i \(0.847222\pi\)
\(450\) 1.95087 0.0919648
\(451\) −19.1543 + 27.3600i −0.901938 + 1.28833i
\(452\) 5.65262 0.265877
\(453\) −29.2189 21.2288i −1.37282 0.997415i
\(454\) −11.0422 + 33.9845i −0.518238 + 1.59497i
\(455\) 0.609683 + 1.87641i 0.0285824 + 0.0879676i
\(456\) −20.6241 + 14.9843i −0.965814 + 0.701705i
\(457\) 14.2748 10.3712i 0.667747 0.485146i −0.201524 0.979484i \(-0.564589\pi\)
0.869270 + 0.494337i \(0.164589\pi\)
\(458\) 4.87077 + 14.9907i 0.227596 + 0.700470i
\(459\) 3.47594 10.6978i 0.162243 0.499333i
\(460\) 1.92715 + 1.40016i 0.0898541 + 0.0652828i
\(461\) −4.51338 −0.210209 −0.105105 0.994461i \(-0.533518\pi\)
−0.105105 + 0.994461i \(0.533518\pi\)
\(462\) 3.70039 + 4.90973i 0.172158 + 0.228421i
\(463\) 31.7059 1.47350 0.736748 0.676167i \(-0.236360\pi\)
0.736748 + 0.676167i \(0.236360\pi\)
\(464\) −4.92174 3.57585i −0.228486 0.166005i
\(465\) 9.64928 29.6974i 0.447475 1.37718i
\(466\) −2.03992 6.27824i −0.0944976 0.290834i
\(467\) −4.13890 + 3.00708i −0.191525 + 0.139151i −0.679416 0.733754i \(-0.737767\pi\)
0.487890 + 0.872905i \(0.337767\pi\)
\(468\) −0.215943 + 0.156891i −0.00998195 + 0.00725231i
\(469\) −2.58195 7.94643i −0.119223 0.366932i
\(470\) 6.77191 20.8418i 0.312365 0.961360i
\(471\) −24.1888 17.5742i −1.11456 0.809776i
\(472\) 3.68449 0.169592
\(473\) 2.18570 + 0.668034i 0.100498 + 0.0307162i
\(474\) 20.4254 0.938168
\(475\) 7.08089 + 5.14457i 0.324893 + 0.236049i
\(476\) 0.210192 0.646906i 0.00963416 0.0296509i
\(477\) 1.71895 + 5.29038i 0.0787053 + 0.242230i
\(478\) 17.8099 12.9396i 0.814604 0.591844i
\(479\) 28.9909 21.0631i 1.32463 0.962399i 0.324766 0.945794i \(-0.394714\pi\)
0.999862 0.0166044i \(-0.00528560\pi\)
\(480\) −3.12562 9.61967i −0.142664 0.439076i
\(481\) −2.68248 + 8.25583i −0.122311 + 0.376434i
\(482\) −8.84493 6.42622i −0.402875 0.292706i
\(483\) −3.68306 −0.167585
\(484\) 1.06920 3.73111i 0.0486000 0.169596i
\(485\) 9.74032 0.442285
\(486\) 7.98244 + 5.79959i 0.362091 + 0.263075i
\(487\) −9.24638 + 28.4574i −0.418994 + 1.28953i 0.489636 + 0.871927i \(0.337130\pi\)
−0.908630 + 0.417603i \(0.862870\pi\)
\(488\) 1.76240 + 5.42410i 0.0797800 + 0.245538i
\(489\) −14.1048 + 10.2477i −0.637841 + 0.463419i
\(490\) −17.7160 + 12.8714i −0.800325 + 0.581470i
\(491\) 4.87992 + 15.0188i 0.220228 + 0.677791i 0.998741 + 0.0501630i \(0.0159741\pi\)
−0.778513 + 0.627628i \(0.784026\pi\)
\(492\) −2.12807 + 6.54952i −0.0959408 + 0.295275i
\(493\) −4.01656 2.91820i −0.180897 0.131429i
\(494\) 5.59029 0.251519
\(495\) 6.35245 + 1.94155i 0.285521 + 0.0872664i
\(496\) 19.2893 0.866113
\(497\) 8.35577 + 6.07082i 0.374808 + 0.272314i
\(498\) 11.7958 36.3036i 0.528581 1.62680i
\(499\) −0.110286 0.339427i −0.00493710 0.0151948i 0.948558 0.316605i \(-0.102543\pi\)
−0.953495 + 0.301410i \(0.902543\pi\)
\(500\) 2.26017 1.64211i 0.101078 0.0734374i
\(501\) −20.3401 + 14.7780i −0.908731 + 0.660232i
\(502\) −8.30333 25.5550i −0.370596 1.14058i
\(503\) 8.06456 24.8202i 0.359581 1.10668i −0.593724 0.804669i \(-0.702343\pi\)
0.953305 0.302008i \(-0.0976570\pi\)
\(504\) 1.37720 + 1.00060i 0.0613455 + 0.0445701i
\(505\) 21.0101 0.934937
\(506\) −6.53298 8.66804i −0.290426 0.385341i
\(507\) 1.93816 0.0860769
\(508\) −2.96021 2.15072i −0.131338 0.0954226i
\(509\) 2.99062 9.20418i 0.132557 0.407968i −0.862645 0.505810i \(-0.831194\pi\)
0.995202 + 0.0978414i \(0.0311938\pi\)
\(510\) 5.26441 + 16.2022i 0.233112 + 0.717445i
\(511\) −7.62487 + 5.53979i −0.337304 + 0.245066i
\(512\) 20.5424 14.9250i 0.907856 0.659596i
\(513\) 5.85288 + 18.0133i 0.258411 + 0.795308i
\(514\) 3.23923 9.96932i 0.142876 0.439728i
\(515\) 23.3496 + 16.9645i 1.02890 + 0.747543i
\(516\) 0.471259 0.0207460
\(517\) 12.2675 17.5230i 0.539525 0.770660i
\(518\) 8.30241 0.364787
\(519\) 0.417516 + 0.303343i 0.0183269 + 0.0133153i
\(520\) −2.47049 + 7.60338i −0.108338 + 0.333430i
\(521\) 6.69927 + 20.6182i 0.293500 + 0.903301i 0.983721 + 0.179702i \(0.0575134\pi\)
−0.690221 + 0.723599i \(0.742487\pi\)
\(522\) 1.50747 1.09524i 0.0659803 0.0479375i
\(523\) 10.3796 7.54121i 0.453868 0.329754i −0.337253 0.941414i \(-0.609498\pi\)
0.791121 + 0.611660i \(0.209498\pi\)
\(524\) 0.649608 + 1.99929i 0.0283783 + 0.0873393i
\(525\) 0.896846 2.76021i 0.0391416 0.120465i
\(526\) −18.4925 13.4356i −0.806312 0.585820i
\(527\) 15.7417 0.685719
\(528\) 0.357327 + 20.3729i 0.0155507 + 0.886618i
\(529\) −16.4976 −0.717288
\(530\) 20.2138 + 14.6862i 0.878032 + 0.637928i
\(531\) −0.285231 + 0.877851i −0.0123780 + 0.0380955i
\(532\) 0.353928 + 1.08928i 0.0153447 + 0.0472262i
\(533\) 8.14681 5.91900i 0.352877 0.256380i
\(534\) 12.5211 9.09713i 0.541842 0.393671i
\(535\) 8.29293 + 25.5230i 0.358535 + 1.10346i
\(536\) 10.4623 32.1996i 0.451902 1.39081i
\(537\) 24.2452 + 17.6152i 1.04626 + 0.760151i
\(538\) −37.5826 −1.62030
\(539\) −20.2094 + 6.96056i −0.870480 + 0.299812i
\(540\) −4.06203 −0.174802
\(541\) 19.1997 + 13.9494i 0.825458 + 0.599730i 0.918271 0.395953i \(-0.129586\pi\)
−0.0928127 + 0.995684i \(0.529586\pi\)
\(542\) −9.56915 + 29.4508i −0.411030 + 1.26502i
\(543\) 8.51394 + 26.2032i 0.365368 + 1.12449i
\(544\) 4.12526 2.99717i 0.176869 0.128503i
\(545\) −29.3075 + 21.2931i −1.25539 + 0.912098i
\(546\) −0.572825 1.76298i −0.0245147 0.0754484i
\(547\) −13.7601 + 42.3492i −0.588339 + 1.81072i −0.00291377 + 0.999996i \(0.500927\pi\)
−0.585425 + 0.810726i \(0.699073\pi\)
\(548\) −1.35641 0.985493i −0.0579431 0.0420982i
\(549\) −1.42876 −0.0609779
\(550\) 8.08694 2.78532i 0.344828 0.118766i
\(551\) 8.35977 0.356138
\(552\) −12.0738 8.77214i −0.513896 0.373367i
\(553\) 1.89093 5.81970i 0.0804107 0.247479i
\(554\) −1.83437 5.64561i −0.0779349 0.239859i
\(555\) 36.0365 26.1821i 1.52966 1.11137i
\(556\) 0.782743 0.568696i 0.0331957 0.0241181i
\(557\) −0.218495 0.672460i −0.00925795 0.0284930i 0.946321 0.323229i \(-0.104768\pi\)
−0.955579 + 0.294736i \(0.904768\pi\)
\(558\) −1.82570 + 5.61892i −0.0772880 + 0.237868i
\(559\) −0.557499 0.405047i −0.0235797 0.0171316i
\(560\) 6.25397 0.264278
\(561\) 0.291610 + 16.6261i 0.0123118 + 0.701953i
\(562\) 9.89130 0.417239
\(563\) −16.6487 12.0960i −0.701659 0.509785i 0.178813 0.983883i \(-0.442774\pi\)
−0.880472 + 0.474098i \(0.842774\pi\)
\(564\) 1.36294 4.19471i 0.0573902 0.176629i
\(565\) 13.1066 + 40.3379i 0.551398 + 1.69703i
\(566\) 19.1550 13.9170i 0.805147 0.584973i
\(567\) 6.44925 4.68565i 0.270843 0.196779i
\(568\) 12.9327 + 39.8028i 0.542645 + 1.67009i
\(569\) −9.77177 + 30.0744i −0.409654 + 1.26078i 0.507292 + 0.861774i \(0.330646\pi\)
−0.916946 + 0.399011i \(0.869354\pi\)
\(570\) −23.2072 16.8610i −0.972042 0.706230i
\(571\) 10.0645 0.421184 0.210592 0.977574i \(-0.432461\pi\)
0.210592 + 0.977574i \(0.432461\pi\)
\(572\) −0.671148 + 0.958671i −0.0280621 + 0.0400840i
\(573\) −31.4218 −1.31267
\(574\) −7.79178 5.66106i −0.325223 0.236288i
\(575\) −1.58337 + 4.87310i −0.0660309 + 0.203222i
\(576\) 2.07337 + 6.38117i 0.0863904 + 0.265882i
\(577\) −28.1851 + 20.4777i −1.17336 + 0.852497i −0.991408 0.130810i \(-0.958242\pi\)
−0.181954 + 0.983307i \(0.558242\pi\)
\(578\) 10.7031 7.77627i 0.445191 0.323450i
\(579\) 6.71660 + 20.6716i 0.279132 + 0.859081i
\(580\) −0.554029 + 1.70513i −0.0230048 + 0.0708015i
\(581\) −9.25179 6.72182i −0.383829 0.278868i
\(582\) −9.15147 −0.379341
\(583\) 14.6788 + 19.4760i 0.607935 + 0.806615i
\(584\) −38.1903 −1.58033
\(585\) −1.62030 1.17722i −0.0669911 0.0486719i
\(586\) −9.23215 + 28.4136i −0.381377 + 1.17376i
\(587\) −6.19911 19.0789i −0.255865 0.787471i −0.993658 0.112444i \(-0.964132\pi\)
0.737793 0.675027i \(-0.235868\pi\)
\(588\) −3.56559 + 2.59055i −0.147042 + 0.106832i
\(589\) −21.4440 + 15.5800i −0.883586 + 0.641963i
\(590\) 1.28117 + 3.94303i 0.0527449 + 0.162332i
\(591\) 9.49827 29.2327i 0.390707 1.20247i
\(592\) 22.2611 + 16.1736i 0.914924 + 0.664731i
\(593\) 22.9665 0.943120 0.471560 0.881834i \(-0.343691\pi\)
0.471560 + 0.881834i \(0.343691\pi\)
\(594\) 17.7007 + 5.41003i 0.726271 + 0.221976i
\(595\) 5.10378 0.209234
\(596\) 4.44121 + 3.22673i 0.181919 + 0.132172i
\(597\) 4.26871 13.1377i 0.174707 0.537692i
\(598\) 1.01131 + 3.11250i 0.0413557 + 0.127280i
\(599\) 4.88139 3.54654i 0.199448 0.144908i −0.483578 0.875301i \(-0.660663\pi\)
0.683027 + 0.730393i \(0.260663\pi\)
\(600\) 9.51419 6.91246i 0.388415 0.282200i
\(601\) −9.05980 27.8832i −0.369557 1.13738i −0.947078 0.321004i \(-0.895980\pi\)
0.577521 0.816376i \(-0.304020\pi\)
\(602\) −0.203666 + 0.626819i −0.00830080 + 0.0255472i
\(603\) 6.86181 + 4.98540i 0.279434 + 0.203021i
\(604\) −6.57505 −0.267535
\(605\) 29.1049 1.02127i 1.18328 0.0415206i
\(606\) −19.7399 −0.801880
\(607\) −28.3892 20.6259i −1.15228 0.837181i −0.163498 0.986544i \(-0.552278\pi\)
−0.988782 + 0.149363i \(0.952278\pi\)
\(608\) −2.65322 + 8.16577i −0.107602 + 0.331166i
\(609\) −0.856608 2.63637i −0.0347115 0.106831i
\(610\) −5.19190 + 3.77213i −0.210214 + 0.152729i
\(611\) −5.21770 + 3.79088i −0.211086 + 0.153363i
\(612\) 0.213370 + 0.656684i 0.00862496 + 0.0265449i
\(613\) 9.41536 28.9775i 0.380283 1.17039i −0.559562 0.828789i \(-0.689031\pi\)
0.939845 0.341602i \(-0.110969\pi\)
\(614\) −10.4302 7.57801i −0.420930 0.305824i
\(615\) −51.6726 −2.08364
\(616\) 7.13750 + 2.18150i 0.287578 + 0.0878950i
\(617\) 16.9062 0.680616 0.340308 0.940314i \(-0.389469\pi\)
0.340308 + 0.940314i \(0.389469\pi\)
\(618\) −21.9380 15.9389i −0.882475 0.641156i
\(619\) 9.01796 27.7544i 0.362462 1.11554i −0.589092 0.808066i \(-0.700515\pi\)
0.951555 0.307479i \(-0.0994854\pi\)
\(620\) −1.75666 5.40644i −0.0705491 0.217128i
\(621\) −8.97045 + 6.51741i −0.359972 + 0.261535i
\(622\) 3.60717 2.62076i 0.144634 0.105083i
\(623\) −1.43282 4.40977i −0.0574048 0.176674i
\(624\) 1.89848 5.84293i 0.0760001 0.233904i
\(625\) 25.0870 + 18.2268i 1.00348 + 0.729072i
\(626\) −15.4154 −0.616125
\(627\) −16.8525 22.3602i −0.673026 0.892979i
\(628\) −5.44314 −0.217205
\(629\) 18.1669 + 13.1991i 0.724364 + 0.526281i
\(630\) −0.591928 + 1.82177i −0.0235830 + 0.0725810i
\(631\) −2.43279 7.48736i −0.0968478 0.298067i 0.890883 0.454233i \(-0.150087\pi\)
−0.987731 + 0.156166i \(0.950087\pi\)
\(632\) 20.0600 14.5744i 0.797943 0.579739i
\(633\) −26.7878 + 19.4625i −1.06472 + 0.773565i
\(634\) −4.37854 13.4758i −0.173894 0.535190i
\(635\) 8.48406 26.1112i 0.336680 1.03619i
\(636\) 4.06832 + 2.95580i 0.161319 + 0.117205i
\(637\) 6.44465 0.255346
\(638\) 4.68522 6.69238i 0.185490 0.264954i
\(639\) −10.4844 −0.414757
\(640\) 15.9375 + 11.5793i 0.629986 + 0.457711i
\(641\) −7.91578 + 24.3623i −0.312655 + 0.962252i 0.664054 + 0.747684i \(0.268834\pi\)
−0.976709 + 0.214568i \(0.931166\pi\)
\(642\) −7.79159 23.9800i −0.307509 0.946417i
\(643\) 10.4942 7.62450i 0.413852 0.300681i −0.361308 0.932447i \(-0.617670\pi\)
0.775159 + 0.631766i \(0.217670\pi\)
\(644\) −0.542449 + 0.394112i −0.0213755 + 0.0155302i
\(645\) 1.09270 + 3.36297i 0.0430248 + 0.132417i
\(646\) 4.46875 13.7534i 0.175821 0.541121i
\(647\) 0.448971 + 0.326196i 0.0176509 + 0.0128241i 0.596576 0.802557i \(-0.296528\pi\)
−0.578925 + 0.815381i \(0.696528\pi\)
\(648\) 32.3020 1.26894
\(649\) 0.0709674 + 4.04619i 0.00278571 + 0.158827i
\(650\) −2.57888 −0.101152
\(651\) 7.11070 + 5.16622i 0.278690 + 0.202480i
\(652\) −0.980809 + 3.01862i −0.0384114 + 0.118218i
\(653\) 8.82697 + 27.1666i 0.345426 + 1.06311i 0.961355 + 0.275311i \(0.0887807\pi\)
−0.615929 + 0.787802i \(0.711219\pi\)
\(654\) 27.5357 20.0059i 1.07673 0.782291i
\(655\) −12.7610 + 9.27138i −0.498612 + 0.362263i
\(656\) −9.86383 30.3578i −0.385118 1.18527i
\(657\) 2.95646 9.09906i 0.115343 0.354988i
\(658\) 4.99032 + 3.62568i 0.194543 + 0.141344i
\(659\) 0.281779 0.0109765 0.00548827 0.999985i \(-0.498253\pi\)
0.00548827 + 0.999985i \(0.498253\pi\)
\(660\) 5.67763 1.95550i 0.221002 0.0761178i
\(661\) −30.9061 −1.20211 −0.601053 0.799209i \(-0.705252\pi\)
−0.601053 + 0.799209i \(0.705252\pi\)
\(662\) −15.3025 11.1179i −0.594748 0.432110i
\(663\) 1.54933 4.76833i 0.0601708 0.185187i
\(664\) −14.3195 44.0710i −0.555706 1.71029i
\(665\) −6.95259 + 5.05135i −0.269610 + 0.195883i
\(666\) −6.81831 + 4.95380i −0.264204 + 0.191956i
\(667\) 1.51233 + 4.65446i 0.0585575 + 0.180221i
\(668\) −1.41440 + 4.35307i −0.0547247 + 0.168425i
\(669\) −8.50593 6.17992i −0.328858 0.238930i
\(670\) 38.0970 1.47182
\(671\) −5.92263 + 2.03988i −0.228641 + 0.0787488i
\(672\) 2.84706 0.109828
\(673\) −14.2303 10.3389i −0.548538 0.398536i 0.278708 0.960376i \(-0.410094\pi\)
−0.827246 + 0.561840i \(0.810094\pi\)
\(674\) −11.1022 + 34.1691i −0.427641 + 1.31614i
\(675\) −2.70001 8.30979i −0.103924 0.319844i
\(676\) 0.285457 0.207397i 0.0109791 0.00797680i
\(677\) 18.8313 13.6817i 0.723745 0.525832i −0.163833 0.986488i \(-0.552386\pi\)
0.887579 + 0.460656i \(0.152386\pi\)
\(678\) −12.3142 37.8993i −0.472925 1.45551i
\(679\) −0.847223 + 2.60748i −0.0325134 + 0.100066i
\(680\) 16.7312 + 12.1559i 0.641613 + 0.466159i
\(681\) −53.9633 −2.06788
\(682\) 0.454246 + 25.8988i 0.0173940 + 0.991714i
\(683\) −14.7596 −0.564759 −0.282380 0.959303i \(-0.591124\pi\)
−0.282380 + 0.959303i \(0.591124\pi\)
\(684\) −0.940601 0.683386i −0.0359648 0.0261299i
\(685\) 3.88753 11.9646i 0.148535 0.457143i
\(686\) −3.97357 12.2294i −0.151712 0.466921i
\(687\) −19.2573 + 13.9913i −0.734714 + 0.533801i
\(688\) −1.76717 + 1.28392i −0.0673726 + 0.0489491i
\(689\) −2.27230 6.99342i −0.0865677 0.266428i
\(690\) 5.18939 15.9713i 0.197557 0.608017i
\(691\) 25.8574 + 18.7865i 0.983662 + 0.714673i 0.958524 0.285011i \(-0.0919974\pi\)
0.0251383 + 0.999684i \(0.491997\pi\)
\(692\) 0.0939524 0.00357153
\(693\) −1.07230 + 1.53167i −0.0407332 + 0.0581834i
\(694\) −24.3417 −0.923998
\(695\) 5.87321 + 4.26714i 0.222784 + 0.161862i
\(696\) 3.47105 10.6828i 0.131570 0.404930i
\(697\) −8.04974 24.7746i −0.304906 0.938403i
\(698\) −1.92875 + 1.40132i −0.0730043 + 0.0530407i
\(699\) 8.06514 5.85967i 0.305052 0.221633i
\(700\) −0.163272 0.502498i −0.00617108 0.0189926i
\(701\) 1.94530 5.98702i 0.0734730 0.226127i −0.907576 0.419889i \(-0.862069\pi\)
0.981049 + 0.193762i \(0.0620690\pi\)
\(702\) −4.51487 3.28025i −0.170403 0.123805i
\(703\) −37.8113 −1.42608
\(704\) 17.7054 + 23.4917i 0.667296 + 0.885376i
\(705\) 33.0942 1.24640
\(706\) 35.5575 + 25.8340i 1.33822 + 0.972277i
\(707\) −1.82748 + 5.62440i −0.0687294 + 0.211527i
\(708\) 0.257853 + 0.793591i 0.00969072 + 0.0298250i
\(709\) 10.2977 7.48169i 0.386737 0.280981i −0.377380 0.926058i \(-0.623175\pi\)
0.764117 + 0.645078i \(0.223175\pi\)
\(710\) −38.0988 + 27.6804i −1.42982 + 1.03883i
\(711\) 1.91952 + 5.90767i 0.0719875 + 0.221555i
\(712\) 5.80591 17.8688i 0.217586 0.669660i
\(713\) −12.5538 9.12088i −0.470144 0.341580i
\(714\) −4.79523 −0.179457
\(715\) −8.39738 2.56656i −0.314044 0.0959840i
\(716\) 5.45583 0.203894
\(717\) 26.8957 + 19.5409i 1.00444 + 0.729768i
\(718\) 0.778937 2.39732i 0.0290697 0.0894673i
\(719\) −5.02037 15.4511i −0.187228 0.576229i 0.812751 0.582611i \(-0.197969\pi\)
−0.999980 + 0.00638149i \(0.997969\pi\)
\(720\) −5.13604 + 3.73155i −0.191409 + 0.139067i
\(721\) −6.57235 + 4.77509i −0.244767 + 0.177834i
\(722\) −0.0107385 0.0330496i −0.000399644 0.00122998i
\(723\) 5.10202 15.7024i 0.189746 0.583979i
\(724\) 4.05787 + 2.94822i 0.150810 + 0.109570i
\(725\) −3.85647 −0.143226
\(726\) −27.3453 + 0.959532i −1.01488 + 0.0356116i
\(727\) 23.3476 0.865913 0.432957 0.901415i \(-0.357470\pi\)
0.432957 + 0.901415i \(0.357470\pi\)
\(728\) −1.82054 1.32270i −0.0674737 0.0490225i
\(729\) 5.31231 16.3496i 0.196752 0.605542i
\(730\) −13.2795 40.8702i −0.491497 1.51267i
\(731\) −1.44216 + 1.04779i −0.0533402 + 0.0387539i
\(732\) −1.04494 + 0.759195i −0.0386222 + 0.0280607i
\(733\) 10.3489 + 31.8506i 0.382245 + 1.17643i 0.938459 + 0.345390i \(0.112253\pi\)
−0.556214 + 0.831039i \(0.687747\pi\)
\(734\) 8.71866 26.8333i 0.321811 0.990434i
\(735\) −26.7539 19.4379i −0.986834 0.716977i
\(736\) −5.02643 −0.185277
\(737\) 35.5621 + 10.8691i 1.30995 + 0.400370i
\(738\) 9.77675 0.359887
\(739\) 20.6920 + 15.0336i 0.761168 + 0.553021i 0.899268 0.437397i \(-0.144100\pi\)
−0.138100 + 0.990418i \(0.544100\pi\)
\(740\) 2.50588 7.71230i 0.0921179 0.283510i
\(741\) 2.60880 + 8.02905i 0.0958365 + 0.294954i
\(742\) −5.68971 + 4.13382i −0.208876 + 0.151757i
\(743\) −19.0569 + 13.8456i −0.699130 + 0.507948i −0.879649 0.475624i \(-0.842222\pi\)
0.180519 + 0.983572i \(0.442222\pi\)
\(744\) 11.0056 + 33.8719i 0.403486 + 1.24180i
\(745\) −12.7287 + 39.1748i −0.466343 + 1.43526i
\(746\) 13.8342 + 10.0511i 0.506506 + 0.367998i
\(747\) 11.6087 0.424740
\(748\) 1.82205 + 2.41752i 0.0666208 + 0.0883933i
\(749\) −7.55384 −0.276011
\(750\) −15.9337 11.5765i −0.581816 0.422714i
\(751\) 11.1965 34.4594i 0.408568 1.25744i −0.509311 0.860582i \(-0.670100\pi\)
0.917879 0.396860i \(-0.129900\pi\)
\(752\) 6.31739 + 19.4429i 0.230371 + 0.709010i
\(753\) 32.8285 23.8513i 1.19634 0.869189i
\(754\) −1.99275 + 1.44782i −0.0725715 + 0.0527263i
\(755\) −15.2454 46.9205i −0.554836 1.70761i
\(756\) 0.353320 1.08741i 0.0128501 0.0395486i
\(757\) −7.82985 5.68872i −0.284581 0.206760i 0.436332 0.899786i \(-0.356277\pi\)
−0.720913 + 0.693026i \(0.756277\pi\)
\(758\) −23.4038 −0.850065
\(759\) 9.40074 13.4281i 0.341225 0.487407i
\(760\) −34.8231 −1.26317
\(761\) −8.43607 6.12916i −0.305807 0.222182i 0.424288 0.905527i \(-0.360524\pi\)
−0.730095 + 0.683345i \(0.760524\pi\)
\(762\) −7.97116 + 24.5327i −0.288765 + 0.888726i
\(763\) −3.15098 9.69771i −0.114073 0.351081i
\(764\) −4.62788 + 3.36235i −0.167431 + 0.121645i
\(765\) −4.19145 + 3.04527i −0.151542 + 0.110102i
\(766\) 6.58966 + 20.2809i 0.238094 + 0.732779i
\(767\) 0.377050 1.16044i 0.0136145 0.0419011i
\(768\) 12.8407 + 9.32932i 0.463349 + 0.336643i
\(769\) 2.00031 0.0721329 0.0360665 0.999349i \(-0.488517\pi\)
0.0360665 + 0.999349i \(0.488517\pi\)
\(770\) 0.147276 + 8.39690i 0.00530745 + 0.302603i
\(771\) 15.8301 0.570105
\(772\) 3.20123 + 2.32583i 0.115215 + 0.0837085i
\(773\) −2.75783 + 8.48772i −0.0991921 + 0.305282i −0.988324 0.152370i \(-0.951309\pi\)
0.889131 + 0.457652i \(0.151309\pi\)
\(774\) −0.206744 0.636293i −0.00743127 0.0228711i
\(775\) 9.89242 7.18726i 0.355346 0.258174i
\(776\) −8.98776 + 6.52999i −0.322642 + 0.234413i
\(777\) 3.87445 + 11.9243i 0.138995 + 0.427782i
\(778\) −14.0135 + 43.1290i −0.502407 + 1.54625i
\(779\) 35.4858 + 25.7819i 1.27141 + 0.923734i
\(780\) −1.81056 −0.0648285
\(781\) −43.4611 + 14.9689i −1.55516 + 0.535631i
\(782\) 8.46590 0.302740
\(783\) −6.75158 4.90531i −0.241282 0.175301i
\(784\) 6.31270 19.4285i 0.225454 0.693875i
\(785\) −12.6208 38.8430i −0.450457 1.38637i
\(786\) 11.9895 8.71089i 0.427652 0.310707i
\(787\) 1.99285 1.44789i 0.0710373 0.0516117i −0.551700 0.834043i \(-0.686021\pi\)
0.622737 + 0.782431i \(0.286021\pi\)
\(788\) −1.72917 5.32183i −0.0615991 0.189582i
\(789\) 10.6670 32.8298i 0.379757 1.16877i
\(790\) 22.5724 + 16.3998i 0.803089 + 0.583478i
\(791\) −11.9385 −0.424483
\(792\) −7.16328 + 2.46719i −0.254536 + 0.0876677i
\(793\) 1.88869 0.0670694
\(794\) 26.4123 + 19.1896i 0.937336 + 0.681015i
\(795\) −11.6599 + 35.8856i −0.413535 + 1.27273i
\(796\) −0.777122 2.39173i −0.0275443 0.0847728i
\(797\) −9.21279 + 6.69349i −0.326334 + 0.237095i −0.738873 0.673844i \(-0.764642\pi\)
0.412540 + 0.910940i \(0.364642\pi\)
\(798\) 6.53228 4.74598i 0.231240 0.168006i
\(799\) 5.15553 + 15.8671i 0.182390 + 0.561338i
\(800\) 1.22396 3.76698i 0.0432737 0.133183i
\(801\) 3.80788 + 2.76658i 0.134545 + 0.0977524i
\(802\) 46.6830 1.64843
\(803\) −0.735588 41.9394i −0.0259583 1.48001i
\(804\) 7.66756 0.270414
\(805\) −4.07020 2.95717i −0.143456 0.104227i
\(806\) 2.41341 7.42772i 0.0850088 0.261630i
\(807\) −17.5385 53.9779i −0.617384 1.90011i
\(808\) −19.3868 + 14.0853i −0.682025 + 0.495520i
\(809\) 20.7755 15.0943i 0.730428 0.530687i −0.159271 0.987235i \(-0.550914\pi\)
0.889699 + 0.456548i \(0.150914\pi\)
\(810\) 11.2320 + 34.5687i 0.394654 + 1.21462i
\(811\) 5.46529 16.8204i 0.191912 0.590645i −0.808087 0.589064i \(-0.799497\pi\)
0.999999 0.00158128i \(-0.000503338\pi\)
\(812\) −0.408272 0.296627i −0.0143275 0.0104096i
\(813\) −46.7643 −1.64009
\(814\) −21.1913 + 30.2697i −0.742754 + 1.06095i
\(815\) −23.8154 −0.834219
\(816\) −12.8573 9.34141i −0.450097 0.327015i
\(817\) 0.927547 2.85470i 0.0324508 0.0998731i
\(818\) 3.37222 + 10.3786i 0.117907 + 0.362880i
\(819\) 0.456076 0.331359i 0.0159366 0.0115786i
\(820\) −7.61045 + 5.52932i −0.265769 + 0.193092i
\(821\) −1.04856 3.22714i −0.0365950 0.112628i 0.931090 0.364789i \(-0.118859\pi\)
−0.967685 + 0.252161i \(0.918859\pi\)
\(822\) −3.65251 + 11.2413i −0.127396 + 0.392085i
\(823\) 28.1776 + 20.4722i 0.982208 + 0.713616i 0.958201 0.286096i \(-0.0923575\pi\)
0.0240073 + 0.999712i \(0.492358\pi\)
\(824\) −32.9186 −1.14677
\(825\) 7.77430 + 10.3150i 0.270666 + 0.359124i
\(826\) −1.16699 −0.0406047
\(827\) 17.9840 + 13.0662i 0.625365 + 0.454355i 0.854792 0.518971i \(-0.173685\pi\)
−0.229426 + 0.973326i \(0.573685\pi\)
\(828\) 0.210329 0.647326i 0.00730943 0.0224961i
\(829\) −5.44222 16.7494i −0.189016 0.581731i 0.810978 0.585076i \(-0.198935\pi\)
−0.999994 + 0.00334471i \(0.998935\pi\)
\(830\) 42.1843 30.6487i 1.46424 1.06383i
\(831\) 7.25246 5.26922i 0.251585 0.182787i
\(832\) −2.74081 8.43535i −0.0950205 0.292443i
\(833\) 5.15171 15.8553i 0.178496 0.549355i
\(834\) −5.51815 4.00917i −0.191078 0.138826i
\(835\) −34.3436 −1.18851
\(836\) −4.87477 1.48992i −0.168597 0.0515299i
\(837\) 26.4608 0.914618
\(838\) 16.5168 + 12.0002i 0.570564 + 0.414539i
\(839\) −3.50209 + 10.7783i −0.120905 + 0.372109i −0.993133 0.116992i \(-0.962675\pi\)
0.872227 + 0.489101i \(0.162675\pi\)
\(840\) 3.56825 + 10.9819i 0.123116 + 0.378913i
\(841\) 20.4815 14.8807i 0.706259 0.513128i
\(842\) −36.1356 + 26.2540i −1.24531 + 0.904773i
\(843\) 4.61593 + 14.2064i 0.158981 + 0.489293i
\(844\) −1.86275 + 5.73296i −0.0641186 + 0.197337i
\(845\) 2.14189 + 1.55618i 0.0736833 + 0.0535341i
\(846\) −6.26161 −0.215279
\(847\) −2.25818 + 7.88020i −0.0775918 + 0.270767i
\(848\) −23.3086 −0.800422
\(849\) 28.9272 + 21.0168i 0.992779 + 0.721296i
\(850\) −2.06150 + 6.34463i −0.0707087 + 0.217619i
\(851\) −6.84026 21.0522i −0.234481 0.721659i
\(852\) −7.66793 + 5.57108i −0.262699 + 0.190862i
\(853\) −6.64024 + 4.82442i −0.227358 + 0.165185i −0.695632 0.718398i \(-0.744876\pi\)
0.468275 + 0.883583i \(0.344876\pi\)
\(854\) −0.558204 1.71797i −0.0191013 0.0587879i
\(855\) 2.69580 8.29680i 0.0921943 0.283745i
\(856\) −24.7630 17.9914i −0.846383 0.614933i
\(857\) 48.7793 1.66627 0.833135 0.553069i \(-0.186544\pi\)
0.833135 + 0.553069i \(0.186544\pi\)
\(858\) 7.88972 + 2.41140i 0.269351 + 0.0823240i
\(859\) 47.9050 1.63450 0.817249 0.576285i \(-0.195498\pi\)
0.817249 + 0.576285i \(0.195498\pi\)
\(860\) 0.520795 + 0.378380i 0.0177590 + 0.0129026i
\(861\) 4.49453 13.8328i 0.153173 0.471419i
\(862\) −6.02841 18.5535i −0.205328 0.631936i
\(863\) 34.6522 25.1763i 1.17957 0.857011i 0.187450 0.982274i \(-0.439978\pi\)
0.992124 + 0.125264i \(0.0399776\pi\)
\(864\) 6.93429 5.03805i 0.235909 0.171398i
\(865\) 0.217845 + 0.670457i 0.00740694 + 0.0227962i
\(866\) −9.08851 + 27.9716i −0.308840 + 0.950512i
\(867\) 16.1634 + 11.7434i 0.548939 + 0.398827i
\(868\) 1.60010 0.0543109
\(869\) 16.3915 + 21.7485i 0.556045 + 0.737768i
\(870\) 12.6394 0.428514
\(871\) −9.07071 6.59025i −0.307349 0.223302i
\(872\) 12.7680 39.2959i 0.432380 1.33073i
\(873\) −0.860029 2.64690i −0.0291076 0.0895839i
\(874\) −11.5326 + 8.37894i −0.390097 + 0.283422i
\(875\) −4.77354 + 3.46818i −0.161375 + 0.117246i
\(876\) −2.67269 8.22570i −0.0903019 0.277921i
\(877\) 5.13006 15.7887i 0.173230 0.533146i −0.826318 0.563203i \(-0.809569\pi\)
0.999548 + 0.0300569i \(0.00956884\pi\)
\(878\) 5.56508 + 4.04327i 0.187812 + 0.136454i
\(879\) −45.1174 −1.52177
\(880\) −15.9628 + 22.8013i −0.538106 + 0.768632i
\(881\) −38.2957 −1.29021 −0.645107 0.764092i \(-0.723187\pi\)
−0.645107 + 0.764092i \(0.723187\pi\)
\(882\) 5.06200 + 3.67776i 0.170446 + 0.123837i
\(883\) −2.69019 + 8.27955i −0.0905321 + 0.278629i −0.986064 0.166369i \(-0.946796\pi\)
0.895531 + 0.444998i \(0.146796\pi\)
\(884\) −0.282056 0.868079i −0.00948657 0.0291966i
\(885\) −5.06530 + 3.68015i −0.170268 + 0.123707i
\(886\) 5.15536 3.74559i 0.173198 0.125835i
\(887\) 0.464261 + 1.42885i 0.0155884 + 0.0479761i 0.958548 0.284931i \(-0.0919706\pi\)
−0.942960 + 0.332907i \(0.891971\pi\)
\(888\) −15.6996 + 48.3183i −0.526843 + 1.62146i
\(889\) 6.25203 + 4.54237i 0.209686 + 0.152346i
\(890\) 21.1415 0.708663
\(891\) 0.622173 + 35.4731i 0.0208436 + 1.18839i
\(892\) −1.91407 −0.0640877
\(893\) −22.7272 16.5123i −0.760537 0.552563i
\(894\) 11.9592 36.8066i 0.399975 1.23100i
\(895\) 12.6503 + 38.9336i 0.422852 + 1.30141i
\(896\) −4.48604 + 3.25930i −0.149868 + 0.108885i
\(897\) −3.99838 + 2.90499i −0.133502 + 0.0969949i
\(898\) 7.49945 + 23.0809i 0.250260 + 0.770221i
\(899\) 3.60904 11.1075i 0.120368 0.370455i
\(900\) 0.433912 + 0.315255i 0.0144637 + 0.0105085i
\(901\) −19.0219 −0.633710
\(902\) 40.5276 13.9586i 1.34942 0.464770i
\(903\) −0.995311 −0.0331219
\(904\) −39.1368 28.4345i −1.30167 0.945719i
\(905\) −11.6300 + 35.7935i −0.386595 + 1.18982i
\(906\) 14.3237 + 44.0839i 0.475874 + 1.46459i
\(907\) 22.5670 16.3959i 0.749323 0.544415i −0.146294 0.989241i \(-0.546734\pi\)
0.895617 + 0.444826i \(0.146734\pi\)
\(908\) −7.94783 + 5.77443i −0.263758 + 0.191631i
\(909\) −1.85510 5.70942i −0.0615299 0.189369i
\(910\) 0.782477 2.40822i 0.0259389 0.0798316i
\(911\) −14.7001 10.6802i −0.487036 0.353852i 0.317007 0.948423i \(-0.397322\pi\)
−0.804043 + 0.594571i \(0.797322\pi\)
\(912\) 26.7603 0.886123
\(913\) 48.1216 16.5741i 1.59259 0.548523i
\(914\) −22.6454 −0.749042
\(915\) −7.84060 5.69653i −0.259202 0.188321i
\(916\) −1.33910 + 4.12133i −0.0442452 + 0.136173i
\(917\) −1.37199 4.22254i −0.0453070 0.139441i
\(918\) −11.6793 + 8.48548i −0.385473 + 0.280062i
\(919\) 10.1412 7.36799i 0.334526 0.243047i −0.407823 0.913061i \(-0.633712\pi\)
0.742349 + 0.670014i \(0.233712\pi\)
\(920\) −6.29968 19.3884i −0.207694 0.639218i
\(921\) 6.01647 18.5168i 0.198250 0.610149i
\(922\) 4.68627 + 3.40477i 0.154334 + 0.112130i
\(923\) 13.8595 0.456190
\(924\) 0.0296413 + 1.68999i 0.000975128 + 0.0555967i
\(925\) 17.4429 0.573518
\(926\) −32.9204 23.9180i −1.08183 0.785996i
\(927\) 2.54836 7.84305i 0.0836992 0.257600i
\(928\) −1.16905 3.59797i −0.0383759 0.118109i
\(929\) −43.4014 + 31.5329i −1.42395 + 1.03456i −0.432850 + 0.901466i \(0.642492\pi\)
−0.991103 + 0.133096i \(0.957508\pi\)
\(930\) −32.4218 + 23.5558i −1.06315 + 0.772426i
\(931\) 8.67459 + 26.6976i 0.284298 + 0.874980i
\(932\) 0.560828 1.72605i 0.0183705 0.0565386i
\(933\) 5.44740 + 3.95777i 0.178340 + 0.129572i
\(934\) 6.56590 0.214843
\(935\) −13.0270 + 18.6078i −0.426029 + 0.608542i
\(936\) 2.28433 0.0746655
\(937\) −9.24364 6.71590i −0.301977 0.219399i 0.426470 0.904502i \(-0.359757\pi\)
−0.728446 + 0.685103i \(0.759757\pi\)
\(938\) −3.31372 + 10.1986i −0.108197 + 0.332995i
\(939\) −7.19385 22.1404i −0.234763 0.722525i
\(940\) 4.87419 3.54130i 0.158978 0.115505i
\(941\) 20.4280 14.8418i 0.665933 0.483828i −0.202729 0.979235i \(-0.564981\pi\)
0.868661 + 0.495407i \(0.164981\pi\)
\(942\) 11.8579 + 36.4948i 0.386350 + 1.18906i
\(943\) −7.93502 + 24.4215i −0.258400 + 0.795273i
\(944\) −3.12902 2.27336i −0.101841 0.0739917i
\(945\) 8.57911 0.279079
\(946\) −1.76547 2.34245i −0.0574005 0.0761597i
\(947\) −32.9370 −1.07031 −0.535154 0.844755i \(-0.679746\pi\)
−0.535154 + 0.844755i \(0.679746\pi\)
\(948\) 4.54301 + 3.30069i 0.147550 + 0.107201i
\(949\) −3.90819 + 12.0282i −0.126865 + 0.390451i
\(950\) −3.47120 10.6833i −0.112621 0.346611i
\(951\) 17.3112 12.5773i 0.561355 0.407848i
\(952\) −4.70945 + 3.42161i −0.152634 + 0.110895i
\(953\) 8.55923 + 26.3426i 0.277261 + 0.853321i 0.988612 + 0.150484i \(0.0480833\pi\)
−0.711352 + 0.702836i \(0.751917\pi\)
\(954\) 2.20613 6.78976i 0.0714260 0.219827i
\(955\) −34.7247 25.2290i −1.12366 0.816390i
\(956\) 6.05227 0.195744
\(957\) 11.7984 + 3.60603i 0.381387 + 0.116566i
\(958\) −45.9909 −1.48590
\(959\) 2.86478 + 2.08138i 0.0925086 + 0.0672114i
\(960\) −14.0640 + 43.2846i −0.453914 + 1.39701i
\(961\) 1.86364 + 5.73569i 0.0601174 + 0.185022i
\(962\) 9.01321 6.54848i 0.290598 0.211132i
\(963\) 6.20356 4.50715i 0.199907 0.145241i
\(964\) −0.928827 2.85863i −0.0299155 0.0920704i
\(965\) −9.17485 + 28.2373i −0.295349 + 0.908990i
\(966\) 3.82414 + 2.77840i 0.123040 + 0.0893935i
\(967\) 32.1552 1.03404 0.517021 0.855973i \(-0.327041\pi\)
0.517021 + 0.855973i \(0.327041\pi\)
\(968\) −26.1715 + 20.4545i −0.841183 + 0.657432i
\(969\) 21.8387 0.701561
\(970\) −10.1134 7.34783i −0.324722 0.235925i
\(971\) −1.89650 + 5.83684i −0.0608617 + 0.187313i −0.976865 0.213858i \(-0.931397\pi\)
0.916003 + 0.401172i \(0.131397\pi\)
\(972\) 0.838255 + 2.57989i 0.0268871 + 0.0827499i
\(973\) −1.65317 + 1.20110i −0.0529982 + 0.0385055i
\(974\) 31.0681 22.5723i 0.995486 0.723263i
\(975\) −1.20347 3.70391i −0.0385419 0.118620i
\(976\) 1.85002 5.69378i 0.0592178 0.182254i
\(977\) −23.5584 17.1162i −0.753701 0.547596i 0.143271 0.989684i \(-0.454238\pi\)
−0.896972 + 0.442087i \(0.854238\pi\)
\(978\) 22.3757 0.715496
\(979\) 19.7347 + 6.03170i 0.630725 + 0.192774i
\(980\) −6.02036 −0.192313
\(981\) 8.37406 + 6.08411i 0.267363 + 0.194251i
\(982\) 6.26296 19.2754i 0.199859 0.615103i
\(983\) −6.34571 19.5301i −0.202397 0.622913i −0.999810 0.0194801i \(-0.993799\pi\)
0.797413 0.603433i \(-0.206201\pi\)
\(984\) 47.6802 34.6417i 1.51999 1.10434i
\(985\) 33.9680 24.6792i 1.08231 0.786343i
\(986\) 1.96900 + 6.05997i 0.0627058 + 0.192989i
\(987\) −2.87857 + 8.85932i −0.0916258 + 0.281995i
\(988\) 1.24339 + 0.903377i 0.0395576 + 0.0287402i
\(989\) 1.75720 0.0558758
\(990\) −5.13113 6.80804i −0.163078 0.216374i
\(991\) 24.3966 0.774985 0.387492 0.921873i \(-0.373341\pi\)
0.387492 + 0.921873i \(0.373341\pi\)
\(992\) 9.70428 + 7.05057i 0.308111 + 0.223856i
\(993\) 8.82694 27.1665i 0.280114 0.862103i
\(994\) −4.09618 12.6067i −0.129923 0.399861i
\(995\) 15.2659 11.0913i 0.483960 0.351618i
\(996\) 8.49019 6.16848i 0.269022 0.195456i
\(997\) 5.83689 + 17.9641i 0.184856 + 0.568929i 0.999946 0.0104061i \(-0.00331243\pi\)
−0.815090 + 0.579335i \(0.803312\pi\)
\(998\) −0.141543 + 0.435625i −0.00448047 + 0.0137895i
\(999\) 30.5374 + 22.1868i 0.966162 + 0.701958i
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 143.2.h.b.92.1 yes 16
11.3 even 5 inner 143.2.h.b.14.1 16
11.5 even 5 1573.2.a.o.1.6 8
11.6 odd 10 1573.2.a.n.1.3 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
143.2.h.b.14.1 16 11.3 even 5 inner
143.2.h.b.92.1 yes 16 1.1 even 1 trivial
1573.2.a.n.1.3 8 11.6 odd 10
1573.2.a.o.1.6 8 11.5 even 5